Easier to explain with a totally new user.
- As a new user login into two different wikis - e.g. enwiki and cawiki.
- The notifications count will be in exact match between two wikis. 'Welcome' notification will be displayed as the Alert from enwiki in cawiki and, of course, in enwiki - correct behavior.
- Generate some notifications for the in enwiki - the number of notifications will be correctly calculated and displayed in enwiki, but not in cawiki.
The counter does not get updated. Not on refreshing the page and not upon log out/log in. Marking notifications as read in enwiki will trigger all kinds of odd counter states:

